I've used a similar technique with my own tools. It helps to save context overall, by deferring the detailed instructions not only to when they're needed, but also to where they're needed.

Simply loading the browser Skill alone, doesn't always mean a browser is actually necessary (or supported). The user might've want them to control their main desktop browser; or the user might be pointing them toward a read-only HTML file that doesn't need rendering; or the sandbox might prevent network access; etc...

Codex is especially 'keen' to use Skills (especially by comparison to Claude), I often see it load Skills which it doesn't go on to use, because the main Skill content says "when not to use this". So I'm sure this is a product design decision to help with those kinds of circumstances.

It's runtime dependent on the browser being used! A skill file wouldn't be able to have this dynamically injected for the browser that's about to be used.

Skill file could indicate general instructions for all browsers. This provides guidance for the browser that's about to actually be used.

Two sources of truth, if playwright updates?

Honestly, this is one of the things OpenAI does pretty well, I think, these tiny design decisions that you wouldn't notice until it becomes super annoying.

I'm guessing, but can be because then the skill will always fetch the latest docs.

That's a pattern I often follow - refer it to the docs, don't include them. Usually it's another markdown, but sometimes it can be the output of something else. This avoids including any of that in context before it's actually needed.